Solar concentrator

ABSTRACT

A collector includes a convergent lens ( 2 ) having a focal distance f and an image focal plane (PFI). The convergent lens ( 2 ) defines one of the walls of a casing ( 1 ) defined by two pairs of side walls ( 4   a,    4   c ), a bottom wall ( 3 ) and a front wall defined by the lens ( 2 ), the side and bottom walls on the inside of the casing being reflective, and the depth p of the casing being lower than the focal distance f of the lens so that after multiple reflections, the ray beam (R 1 , R 2 ) thus reflected is concentrated on a final image focus (I′) located inside the casing, the collector including a mobile receptor ( 6   a ) held inside the concentrated beam or in a position at least intersecting the beam by elements controlling the movement of the collector ( 6   a ) with that of the beam.

The subject of the present invention is a solar concentrator of the typecomprising, as collector, a convergent lens having, in a manner knownper se, a focal distance and an image focal plane on which areconcentrated, along a line, called “primary image focus”, the beam ofthe solar rays that said lens receives, said concentrated beam movingwith the trajectory of the sun. Such a lens is said to be “linear” inthat its focus is a line.

To take account of the variation of the direction of the solar rays inthe course of the day and in the course of seasons, the known solarconcentrators either use costly parabolic mirrors or are included inpivoting and motorized equipment that is complicated and fragile.

The present invention proposes to provide a simple and effectivesolution to remedy these drawbacks.

To this end, the present invention provides a solar concentrator of theabovementioned type, in which said convergent lens forms one of thewalls of a chamber defined by:

two pairs of side walls, a bottom wall and a front wall formed by saidlens, the side walls of each pair being parallel to each other, and eachpair of side walls being perpendicular to the other pair,

the side and bottom walls, inside the chamber, being reflective,

the depth p between the front wall and the bottom wall being less thanthe focal distance f of the lens,

such that, after multiple reflections, the duly reflected beam of raysis concentrated on a line called “final image focus” symmetrical to saidprimary image focus relative to said bottom wall and belonging to a“near image focal plane” itself symmetrical to said image focal planerelative to said bottom wall, but located inside said chamber,

said concentrator enclosing a mobile receiver maintained within saidconcentrated beam, or in a position at least secant to said beam, bymeans servo-controlling the movement of said receiver to the movement ofsaid beam.

In a preferred embodiment, the front and bottom walls of the chamber areperpendicular to the side walls; in other words, the chamber takes theform of a rectangular parallelepiped.

In this particular case, the depth p of the chamber satisfies therelation:

p=0.5*(f+e+b)

where:

-   -   e is the penetration thickness of the lens in the chamber, and    -   b is the distance between the lens and the near image focal        plane or useful operating distance,

said concentrator enclosing a mobile receiver maintained within saidconcentrated beam, or in a position at least secant to said beam, bymeans servo-controlling the movement of said receiver to the movement ofsaid beam.

Thus, the structure of the concentrator according to the invention makesit possible to follow the trajectory of the sun, by servo-controlling onthis trajectory, not the orientation of the chamber, but the position ofthe receiver in the chamber. It follows from this, on the one hand, thatthe servo-control means can be considerably lighter than if the entirechamber had to be moved and, on the other hand, that the mobile element(the receiver) is protected from the external medium by the chamber.

In practice, the receiver is fitted to move, in the near image focalplane of said lens or in a plane parallel to said near image focalplane.

The servo-control means that can be used are within the area ofcompetence of those skilled in the art. They can in particular applysimilar principles to those implemented in the known concentrators. Itwill be understood that, in the absence of solar rays or when there isinsufficient radiation, the receiver can remain temporarily immobile inthe chamber and be repositioned relative to the concentrated beam whenthe radiation has returned to a sufficient level.

In one possible embodiment, to control the speed and the direction ofmovement of said receiver, the latter is provided with a photon fluxmeter adapted to send signals to driving means to which the receiver issubjected.

For the position of the receiver to be optimal, that is, for it toreceive all the concentrated beam, the center of the receiver must belocated within an area that affects an extent ranging from +k to −keither side of said near image focal plane, median to said area, ksatisfying the relation:

$k = \frac{r}{\sin \left\lbrack {A\; {\tan \left( \frac{d}{f} \right)}} \right\rbrack}$

where:

-   -   r is the radius of the transverse section of the receiver if        this section is circular or of the circle inscribed in the        section of the receiver if this section is not circular, given        that the expression “center of the receiver” is understood to        mean the straight line parallel to the final image focus and        which passes through the center of said circle;    -   sin[A tan] stands for sinus[arc tangent];    -   d is the distance between the optical axis of the lens and the        edge of the lens, taken in the plane containing said optical        axis and which is perpendicular to the bottom of the chamber and        orthogonal to the final image focus.

However, it is possible to place the center of the receiver outside thisoptimal area while still obtaining an acceptable result, for example aneconomically acceptable result, if the loss of performance is offset bya significant reduction in the cost of the concentrator.

The convergent lens can take various forms, provided that itconcentrates the solar rays along a line. Thus, the convergent lens canbe flat-convex, biconvex or convergent meniscus.

Preferably, and without being exclusive, the convergent lens will be aFresnel lens in the interests of reducing the footprint and weight ofthe lens. A Fresnel lens also has the advantage of being less absorbentto the rays that pass through it than other lenses.

In the case of a flat-convex Fresnel lens, that is, a lens that has aflat face and a sawtooth face, said lens will, preferably, be fitted sothat its flat face faces the outside of said chamber.

This orientation has the advantage of placing the face of the lens thatis most likely to trap dirt inside the chamber, the flat, outer faceobviously being easier to clean. For the same reason, if the Fresnellens is biconvex, that is, a lens having a smooth convex face and asawtooth face, the lens will, preferably, be fitted so that its convexface faces the outside of said chamber.

In another embodiment, the lens can be a convergent meniscus lens, thatis, a lens that has a convex face and a concave face; such a lens willnecessarily be fitted so that its convex face faces the outside of saidchamber.

The receiver is advantageously a heat pipe covered with a material, theheat absorption coefficient of which is greater than the heat emissioncoefficient.

In a particular embodiment of the invention, more particularly intendedfor solar power plants, the heat pipe takes the form of a pipe, possiblyflexible, included in a pipe under vacuum, to limit the thermal loss.

The heat pipe is advantageously connected to an extraction exchanger fedwith a heat-carrying fluid to exploit the heat obtained, for example toheat water or another fluid, to heat a device or to generate solar cold.

In another embodiment, the receiver is an extraction exchanger fed witha heat-carrying fluid.

In yet another embodiment, the receiver can be a photovoltaic cellreceiver.

In a preferred embodiment, the receiver can occupy two positions, namelya service position in which it receives a certain thermal energy and aretracted position in which it receives a lesser thermal energy than inthe service position, retracting means being able to move the receiverfrom its service position to its retracted position, where there is riskof overheating, for example, in the case where the circulation ofheat-carrying fluid is no longer in the extraction exchanger.

The receiver can be connected to a Stirling engine, that is, an enginethat exploits a temperature difference between a hot source and a coldsource, notably for the purpose of producing electricity.

Preferably, the surfaces of the lens are treated to reduce theirpotential degradation over time, degradations that can consist, mainlyon the outer side, in dirt, and on the inner side, in the deposition ofmetal particles ejected from the reflective surfaces. Such a treatmentcan consist of a non-stick surface treatment increasing the wettabilityand obtained by applying thin layers consisting of compounds based onSiOx (SiO₂ etc.) and/or of coatings that make it possible to reduce theattachment of different pollutants, such as TiO₂-type photocatalyticcompounds.

It can also be a protection against ageing of the lens material,obtained by deposition on the outer surface of the lens of conventionalanti-glare-treatment optical layers. Such an anti-glare treatment alsohas the advantage of reducing the reflection, by the lens, of the raysthat it receives on certain incidences.

The same applies to the reflective walls of the chamber which willadvantageously be treated to reduce their potential degradation overtime.

Concerning the reflective walls, as a variant, they can be made ofreflective panels that can be removed for the purposes of cleaning,replacement or complete flat-packing of the chamber for transport ormoving purposes.

The invention will be better understood from reading the followingdescription, given with reference to the appended drawings in which:

FIG. 1 is a cut-away perspective diagrammatic view of an embodiment of achamber according to the invention,

FIGS. 2 a, 2 b and 2 c illustrate various types of lenses that can beused according to the invention with identification of the thickness e;

FIGS. 3 a and 3 b are diagrams of one embodiment of the chamberaccording to the invention, illustrating the effect of the usefuldistance b on the depth of the chamber;

FIGS. 4 a and 4 b are diagrams of an embodiment of a chamber accordingto the invention, seen in cross section in a plane perpendicular to thegeneral direction of the lens, and illustrating the path of the solarrays along two different incidences;

FIGS. 5 a and 5 b are diagrams illustrating the parameter k and theoptimal positioning area of the receiver, FIG. 5 b being a larger-scaleview of the area of the final image focus of FIG. 5 a, and

FIG. 6 is a diagram illustrating one embodiment of a driving mechanismfor the heat pipe.

As can be seen in FIG. 1, the chamber 1, in this embodiment of theinvention, is of rectangular parallelepipedal form, consisting of afront wall comprising a linear convergent lens 2, a rear or bottom wall3 and side walls 4 a-d. The internal faces of the side walls 4 a-d andbottom wall 3 of the chamber 1 are reflective, either coated with areflective film or lined with a removable reflective wall.

The side wall 4 b includes a slot such as 5, in which a heat pipe 6 canslide in a plane parallel to the general plane of the lens 2, the heatpipe being supported, opposite the slot, by appropriate means (notrepresented) allowing this sliding movement.

The heat pipe 6 is clad with a material having a thermal dissipationcoefficient less than its thermal absorption coefficient to limit thelosses, as much as possible. An extraction exchanger 7, fed with fluidthat is cold on 7 a and leaves hot on 7 b, evacuates the heat from theheat pipe for appropriate exploitation.

The chamber 1 is prolonged by a housing 8 (the start of which is shownby broken lines in FIG. 1) for the extraction exchanger 7 and a drivingmechanism not represented in FIG. 1 (see FIG. 6). The housing 8 can havethe same rectangular section as the chamber 1 and be closely connectedthereto to avoid any ingress of rainwater or dust. It can advantageouslybe opaque to slow down the ageing of the flexible pipes 9 a and 9 b(FIG. 6).

The lens 2 of the chamber 1 is struck by the solar rays along anincidence that varies with the time of day, the season, and so on, andtwo such different incidences are illustrated by the rays R and R′.

To return to the optical plane, FIG. 4 a, which represents the chamber 1without the heat pipe 6 or the extraction exchanger 7 for clarity ofrepresentation, it can be seen that the lens 2 comprises a flat-convexFresnel lens 2, the flat face of which faces the outside of the chamber.The thickness of the lens is exaggerated in the figure also in theinterests of clarity. The lens 2 has an optical axis AA, a focaldistance f greater than the depth p of the chamber 1 and an image focalplane PFI which is beyond the bottom 3 of said chamber 1.

As indicated above, the depth p of the chamber must satisfy therelation:

p=0.5*(f+e+b)

This relation is explained by reference to FIGS. 2 a-2 c and 3 a-3 b.

FIGS. 2 a, 2 b and 2 c respectively show

-   -   a flat-convex lens 2 a, in this case a Fresnel lens,    -   a biconvex lens 2 b, and    -   a meniscus lens 2 c,

forming one of the walls of a chamber, of which the beginning of theside walls 4 a and 4 c can be seen.

In the case of the Fresnel lens 2 a, the flat face of the lens coincideswith the plane FF passing through the adjacent edge of the side walls 4a-4 d, and the penetration thickness e is the distance between thisplane FF and the plane TT tangential to the most prominent part of thelens inside the chamber.

In the case of the biconvex lens 2 b, one of the convex faces of thelens projects outside the chamber 1 and the other convex face projectstowards the interior of the chamber. The penetration thickness e is thedistance between the median plane of the lens, a plane that coincideswith the plane FF, passing through the adjacent edge of the side walls 4a-4 d, and the plane TT tangential to the most prominent part of thelens inside the chamber.

In the case of the meniscus lens 2 c, no part of the lens penetratesinto the chamber (apart from the lens fixing), so the thickness e ismore or less zero.

As can be seen from FIGS. 3 a and 3 b, where the lens has beendiagrammatically represented in the form of a simple rectangledesignated by 2 a-c, to show that it can be any one of the lens types 2a, 2 b or 2 c illustrated in FIGS. 2 a to 2 c, the parameters needed todetermine the depth of the chamber are indicated.

In FIGS. 3 a and 3 b, it can be seen that the lens 2 a-c has a thicknesse and a focal distance f, a distance that determines the image focalplane PFI.

In the case of FIG. 3 a, a useful distance b1 is provided, a distancethat needs to allow for the accommodation of the receiver, in otherwords the heat pipe 6 in the embodiment of FIG. 1, and its supportopposite the slot 5, taking into account the heat sensitivity of thelens, therefore of the material of the lens.

Initially, for simplicity, it will be assumed that the receiver 6 is inthe PFIR plane located at e+b1 of the plane FF, which is a particularcase, as will be seen in light of FIGS. 5 a and 5 b. The bottom 3 of thechamber must also be equidistant from the PFIR plane and the PFI plane.

In the case where b=b₁ (FIG. 3 a), the distance between PFIR and PFI is2*x₁.

In the case where b=b₂ with b₂>b₁ (FIG. 3 b), the distance between PFIRand PFI is 2*x₂.

The choice of b is within the scope of those skilled in the art. Itdepends on the footprint of the receiver 6 and means that are associatedwith it, as well as the lens material.

As an example, for a flat-convex Fresnel lens of 50 cm×100 cm, made ofglass with a refractive index n=1.5, a focal distance f of 80 cm and athickness e=1.5 cm, observing a useful distance b=15 cm, the depth p ofthe chamber 1 will be equal to the product 0.5(f+e+b)=0.5*(80+1,5+15)=48.25 cm. Obviously, these values are given only to enable thereader to clearly understand the principle of the invention. Inpractice, these values can be other values and the depth of the chambercan be even smaller relative to the focal distance.

To return to FIG. 4 a, in the absence of the bottom of the chamber,solar rays striking the lens 2 parallel to the ray R would beconcentrated on a primary image focus, in the image focal plane PFI.However, the reflective side walls, such as 4 a, and the reflectivebottom 3 of the chamber stop the rays R and reflect them until they areconcentrated on a final image focus, in a near image focal plane PFIRparallel to the image focal plane PFI, but inside the chamber 1. In FIG.4 a, this final image focus is seen in cross section, therefore in theform of a dot I.

FIG. 4 b is similar to FIG. 4 a, except that it illustrates anotherdirection of impact of the rays, such as R′, on the lens 2. As can beseen, after multiple reflections, these rays R′ are concentrated on afinal image focus, also located in the plane PFIR, and this final imagefocus is seen in cross section in FIG. 4 b, therefore in the form of adot I′.

Thus, the final image focus of the rays R and that of the rays R′ arelocated in the same plane PFIR, but on two different lines or, toexpress it differently, the linear final image focus movestranslation-wise in the plane PFIR following the trajectory of the sun.

The heat pipe 6 which, in the particular case considered, is positionedin the plane PFIR, moves to follow this translation movement of thelinear final image focus. To this end, motor means are provided,servo-controlling the movement of the heat pipe to the trajectory of thesun, or more precisely to the trajectory of the beam of raysconcentrated towards the final image focus. This servo-control takesinto account the place where the chamber is installed, the season, thetime of day, and so on.

As indicated above, the heat pipe can, furthermore, be subject toretracting means adapted to move it, if necessary, out of its serviceposition, to avoid overheating. To this end, the retracting means movethe heat pipe from its service position where it receives a certainthermal energy to a retracted position where it receives a lesserthermal energy than in the service position.

As can be seen from the example with figures indicated above, theinvention considerably reduces the distance needed between the lens andthe heat pipe. Without the invention, in the example given, thisdistance would be f−e=80−1.5=78.5 cm, whereas according to the inventionand still in the example concerned, it is only 48.25 cm.

Referring to FIG. 5 a, the chamber 1 is shown with its lens 2 and itsbottom 3. Also to be seen in this figure is a receiver 6 a which can bepresented in the form of an appliance of circular section of radius r(see FIG. 5 b), but which is not necessarily circular. If the receiveris not of circular section, the circle inscribed in the non-circularsection is taken into account. Also identified in this figure is thedistance d used in calculating the value k.

R₁ and R₂ indicate solar rays forming the outer limits of the beam ofrays striking the lens 2 with a zero incidence. The beam bounded by R₁and R₂ converges towards the plane PFI but is stopped and reflected bythe bottom 3 to converge in a concentrated beam towards the plane PFIRthat it crosses along a line seen in cross section at I″, correspondingto the final image focus, to diverge beyond the plane PFIR. It will beunderstood that the concentrated beam thus delimits, either side of thefinal image focus I″, two crossed planes with an angle between them ofα.

As long as these planes are tangential to the receiver (position 6a-FIGS. 5 a and 5 b) or secant to the receiver (position 6 b-FIG. 5 b),the receiver receives all the concentrated beam. However, if thereceiver is indeed located between these planes, without these planesbeing secant or tangential to it (position 6 c-FIG. 5 d), a part of theconcentrated beam, namely the part that is between, respectively, theplane of the rays R₁ and R₂ and the tangents T₁ and T₂ to the receiver 6c, does not strike the receiver.

Thus, as can be seen in FIG. 5 b, for the receiver to occupy an optimumposition, the line passing through the center of the receiver andparallel to the final image focus I″ (line Ca for the receiver inposition 6 a, line Cb for the receiver in position 6 b) must be locatedin an area of extent E ranging from +k to −k, either side of the planePFIR, k necessarily satisfying the relation:

$k = \frac{r}{\sin \left\lbrack {A\; {\tan \left( \frac{d}{f} \right)}} \right\rbrack}$

where r, d and f are as defined above, the center of the receiverpossibly being able to coincide with said final image focus I″(abovementioned particular case).

A position of the receiver such as 6 c, where the line Cc is outside thearea of extent E, is not however a situation beyond the scope of theinvention; this position can be acceptable, even though the receiverdoes not receive all of the concentrated beam, for example if it is lesscostly to position the receiver at 6 c than at 6 a or 6 b.

Actually, the positions 6 a, 6 b and 6 c could equally be on the otherside of the plane PFIR.

FIG. 5 b shows, furthermore, for the receiver 6 a, a service position(in this case, within the concentrated beam and tangential to the planesbounding this beam) and a retracted position, illustrated at 6 a′ wherethe receiver is totally outside the concentrated beam. The position 6 ccould also be considered to form the retracted position of the receiver6 a.

Referring to FIG. 6, the references E1 and E8 respectively designate theinternal space of the chamber 1 and the internal space of the housing 8,separated by the partition 4 b, slotted at 5. The heat pipe 6 and theexchanger 7 with its supply of cold fluid on 7 a and its discharge ofhot fluid on 7 b are located therein, as represented in FIG. 1. Morespecifically, this supply and this discharge take place via flexiblepipes, respectively 9 a and 9 b, connected to nozzles, respectively 10 aand 10 b, themselves in fluid communication with the inside of theexchanger 7. Flexible pipes 9 a and 9 b are used, obviously, to enablethe heat pipe 6 to move.

To obtain this movement, the heat pipe 6 is connected, via a collar 11provided with a fork 12 a, 12 b, to the rotation axis of a gear 13 whichmeshes with a rack 14, the gear 13 itself being driven rotation-wise bya motor 15.

A photon flux meter is diagrammatically represented as 16, making itpossible to send signals to said motor means to control the directionand the speed of rotation of the gear 13, and therefore of the heat pipe6.

Obviously, the invention is not limited to the embodiments described andrepresented. Thus, the lens and the bottom of the chamber are notnecessarily perpendicular to the side walls of said chamber, and notnecessarily parallel to each other. Instead of incorporating a heatpipe, the chamber could contain an extraction exchanger fed withheat-carrying fluid or a linear volume clad with photovoltaic cells,both mobile as described for the heat pipe. Moreover, it is possible tojuxtapose several lenses, each forming a face of a “sub-chamber”, theduly juxtaposed sub-chambers having components in common, notably acommon driving mechanism, to limit the quantity of constituent materialsused and to reduce the number of servo-controls for moving the receiver.

1-18. (canceled)
 19. A solar concentrator of the type comprising, ascollector, a convergent lens having a focal distance and an image focalplane, on which are concentrated, along a line, called “primary imagefocus”, the beam of the solar rays that said lens receives, saidconcentrated beam moving with the trajectory of the sun, wherein saidconvergent lens forms one of the walls of a chamber defined by: twopairs of side walls, a bottom wall and a front wall formed by said lens,the side walls of each pair being parallel to each other, and each pairof side walls being perpendicular to the other pair, the side and bottomwalls, inside the chamber, being reflective, the depth between the frontwall and the bottom wall being less than the focal distance of the lens,such that, after multiple reflections, the duly reflected beam of raysis concentrated on a line called “final image focus” symmetrical to saidprimary image focus relative to said bottom wall and belonging to a“near image focal plane” itself symmetrical to said image focal planerelative to said bottom wall, but located inside said chamber, saidconcentrator enclosing a mobile receiver maintained within saidconcentrated beam, or in a position at least secant to said beam, bymeans servo-controlling the movement of said receiver to the movement ofsaid beam.
 20. The concentrator as claimed in claim 19, wherein saidchamber is rectangular parallelepiped and wherein the depth p of thechamber, for this purpose, satisfies the relationp=0.5*(f+e+b) where: e is the penetration thickness of the lens in thechamber, and b is the distance between the lens and the near image focalplane or useful operating distance.
 21. The solar concentrator asclaimed in claim 19, wherein the center of said receiver is locatedwithin an area that affects an extent ranging from +k to −k either sideof said near image focal plane, median to said area, k satisfying therelation:$k = \frac{r}{\sin \left\lbrack {A\; {\tan \left( \frac{d}{f} \right)}} \right\rbrack}$where: r is the radius of the transverse section of the receiver if thissection is circular or of the circle inscribed in the section of thereceiver if this section is not circular, given that the expression“center of the receiver” is understood to mean the straight lineparallel to the final image focus and which passes through the center ofsaid circle; sin[A tan] stands for sinus[arc tangent]; d is the distancebetween the optical axis of the lens and the edge of the lens, taken inthe plane containing said optical axis and which is perpendicular to thebottom of the chamber and orthogonal to the final image focus.
 22. Theconcentrator as claimed in claim 19, wherein said convergent lens isflat-convex, biconvex or convergent meniscus.
 23. The concentrator asclaimed in claim 19, wherein said convergent lens is a Fresnel lens. 24.The concentrator as claimed in claim 19, wherein said convergent lens isa flat-convex Fresnel lens fitted so that its flat face faces theoutside of said chamber.
 25. The concentrator as claimed in claim 19,wherein said convergent lens is a biconvex Fresnel lens, fitted so thatits convex smooth face faces the outside of said chamber.
 26. Theconcentrator as claimed in claim 19, wherein said receiver is a heatpipe covered with a material, the heat absorption coefficient of whichis greater than the heat emission coefficient.
 27. The concentrator asclaimed in claim 19, wherein said receiver is a heat pipe covered with amaterial, the heat absorption coefficient of which is greater than theheat emission coefficient, said heat pipe taking the form of a pipeincluded in a pipe under vacuum.
 28. The concentrator as claimed inclaim 19, wherein said receiver is a heat pipe covered with a material,the heat absorption coefficient of which is greater than the heatemission coefficient, said receiver being connected to an extractionexchanger fed with a heat-carrying fluid.
 29. The concentrator asclaimed in claim 19, wherein the receiver is a photovoltaic cellreceiver.
 30. The concentrator as claimed in claim 19, wherein saidreceiver is an extraction exchanger fed with heat-carrying fluid. 31.The concentrator as claimed in claim 19, wherein said receiver canoccupy two positions, namely a service position in which it receives acertain thermal energy and a retracted position in which It receives alesser thermal energy than in the service position.
 32. The concentratoras claimed in claim 19, wherein the receiver is connected to a Stirlingengine.
 33. The concentrator as claimed in claim 19, wherein thesurfaces of the lens and/or the reflective walls of the chamber aretreated to reduce the potential degradation of their material over time.34. The concentrator as claimed in claim 19, wherein the outer surfaceof the lens includes an anti-glare treatment.
 35. The concentrator asclaimed in claim 19, wherein the reflective walls are made of removablereflective panels.
 36. The concentrator as claimed in claim 19, wherein,to control the speed and the direction of movement of the receiver, thelatter is provided with a photon flux meter adapted to send signals todriving means to which said receiver is subjected.
 37. The solarconcentrator as claimed in claim 20, wherein the center of said receiveris located within an area that affects an extent ranging from +k to −keither side of said near image focal plane, median to said area, ksatisfying the relation:$k = \frac{r}{\sin \left\lbrack {A\; {\tan \left( \frac{d}{f} \right)}} \right\rbrack}$where: r is the radius of the transverse section of the receiver if thissection is circular or of the circle inscribed in the section of thereceiver if this section is not circular, given that the expression“center of the receiver” is understood to mean the straight lineparallel to the final image focus and which passes through the center ofsaid circle; sin[A tan] stands for sinus[arc tangent]; d is the distancebetween the optical axis of the lens and the edge of the lens, taken inthe plane containing said optical axis and which is perpendicular to thebottom of the chamber and orthogonal to the final image focus.